# [EM] Is strategic voting a bad thing, really?

wclark at xoom.org wclark at xoom.org
Mon Apr 5 23:42:02 PDT 2004

```Bart Ingles wrote:
> In general, it's a good thing.  However the NEED or INCENTIVE for
> strategic voting is sometimes a bad thing, if it results in Duvergerian
> equalibria (Plurality, Runoff, Instant Runoff), or in artificial ties or
> "random" outcomes (Borda).

I'm wondering if even these cases are examples of errors (or
inefficiencies) in strategy implementation, rather than the result of
strategy (or of the need for strategy) in general.  The support for the
two party-system coming out of plurality, for example, strikes me as owing
quite a bit to the *inability* of voters to effectively strategize, and
the need for two obvious "name brand" alternatives to serve as organizing
factors in strategy development.

What I have in mind (and what started me down this line of thought in the
first place) is what various methods would look like under the assumption
of complete or perfect information.  The zero information scenario has the
nice feature that the best strategy is to vote sincerely -- but I'm
wondering if the same thing can be achieved through perfect information.

Consider a simple case with 3 candidates under plurality:

A>B>C:K_1
A>C>B:K_2
B>C>A:K_3
B>A>C:K_4
C>A>B:K_5
C>B>A:K_6

(Where K_1 through K_6 are the proportion of voters out of 100 that
sincerely preferred each respective ordering.)

In a sincere election, the winner would be determined by whichever of
(K_1+K_2), (K_3+K_4), or (K_5+K_6) was the greatest.  If any one of these
sums turned out to be greater than 50, then strategy would be irrelevant
to the outcome.

Assuming strategy isn't irrelevant -- and assuming the following claim:

(Uniform Strategic Blocs:)  Any optimal strategy for a given voter will
apply uniformly (i.e. non-probabilistically) for all voters within that
preference bloc.  For example, the optimal strategy for all A>B>C voters
will be the same, so that they will all vote the same way if they were to
vote according to that strategy.

-- THEN, any strategic rearranging of the partial sums for each candidate
will still be made up of K_1 through K_6.  That is, the following are the
only ways in which the sums could be arranged:

(K_1+K_2+K_3+K_4+K_5+K6),(0),(0)
(K_1+K_2+K_3+K_4+K_5),(K6),(0)
(K_1+K_2+K_3+K_4),(K5+K6),(0)
(K_1+K_2+K_3+K_4),(K5),(K6)
(K_1+K_2+K_3),(K_4+K5+K6),(0)
(K_1+K_2+K_3),(K_4+K5),(K6)
etc...

This type of partitioning should result in a finite and highly ordered
structure to the space of possible outcomes for the election, which might
be exploited to significantly simplify the mathematics involved -- and
more importantly, which might introduce various discontinuities
(discreteness) that will tease out subtle secondary aspects of the
particular election method being used.

I'm not sure how plausible the Uniform Strategic Blocs assumption is, but
for it to be violated it would have to be the case that sometimes the best
strategy for a bloc of voters with identical preferences would be for some
of them to vote one way while others vote a different way.  That sort of
symmetry breaking would require a randomizing element (e.g. a coin flip in
the voting booth) and I'm skeptical that an optimal strategy would include
such features.  I'm open to argument either way, though.

Putting aside the Uniform Strategic Bloc assumption for a moment, there's
the issue of how to realize perfect information in an actual election.
I've been implicitly assuming that perfect information also includes
complete knowledge of optimal strategies, but perhaps it would be better
to treat this by itself.  In any event, I'd like to suggest an approach
that might provide for both perfect information as well as implementation
of the appropriate optimal strategy, for each and every voter in an
election.

The idea is that each voter would indicate their sincere preferences on a
"pre-ballot" that would then be turned over to a "strategy agent" which
would produce the final (strategically optimal) ballot.  The strategy
agent might be a computer program of some sort, which would have at its
disposal (among other things) the pre-ballots of all other voters.

Voters would be encouraged to cast sincere pre-ballots by generating
sufficient trust in the effectiveness of the strategy agents (that is, if
voters believe that the strategy agent will do at least as good a job in
devising a voting strategy as they themselves would, then they have little
point, however.

It might be the case that a sort of "meta-stragegy" could evolve, in which
it would benefit some voters to manipulate the relative values of K_1
through K_6, and thus the optimal strategies determined by the strategic
agents for each preference bloc.  It's not immediately clear to me how
such a meta-strategy could possibly work, however, since it would involve
putting your vote in the employ of a voting bloc that held sincere
preferences different than your own.  It almost seems as if it would
involve "out-smarting" the strategy agents -- which by design already have
full knowledge of everybody's preferences via the pre-ballots.

In any event, it at least seems *possible* to me that such a
perfect-information election method could be implemented in practice
(although it might be enormously complicated) -- so given that, we come
back to the question of whether it would be at all *useful* to do so.

Does anyone know of any additional analysis or research into the question
of how various election methods behave under an assumption of perfect
information?  (And thanks to those who have already posted such
references.)

-Bill Clark

--
Ralph Nader for US President in 2004